feat: choose a product's category from the ones T5DE has seen

A product can be filed under another IMVU category than its parent's: any category path the hub has seen on a
revision's parent (and each step of it), within the parent's top-level category, so it stays the same kind of
product (the proxy tells clothing, furniture and rooms apart by category). It's an info field like the others:
lockable, in the history, undone by the same rules. Lists filter by the chosen path, and products show it.

Co-Authored-By: Claude Opus 5.5 <[email protected]>

apps/api/test/products.test.ts

@@ -280,6 +280,28 @@ test("derived products carry their IMVU parent's image and categories", async ()
   expect(await page(missingID)).toMatchObject({ parent: 7999, image: null, categories: [] });
   expect(await hub.products.fillParentInfo(50)).toBe(0);
 
+  // A product can be filed under another category the hub has seen, in its parent's top-level category: a jacket
+  // made from a plain top goes under Coats & Jackets, never under Hair or Body (another kind of product).
+  imvuProducts.set(7004, { ...coat, category_path: coat.category_path.slice(0, 3) });
+  const jacketID = await upload("Dresser Jacket", 7004);
+  for (let i = 0; i < 100 && (await page(jacketID)).categories.length === 0; i++) await Bun.sleep(20);
+  const { choices, parent } = (await call(dresser, "GET", `/api/v1/products/${jacketID}/categories`)).json;
+  expect(parent.map((c: any) => c.id)).toEqual([106, 40, 128]);
+  expect(choices.map((c: any) => c.at(-1).id).sort()).toEqual([106, 128, 40, 716]);
+  expect((await call(undefined, "GET", `/api/v1/products/${jacketID}/categories`)).status).toBe(401);
+  expect((await call(dresser, "PATCH", `/api/v1/products/${jacketID}`, { category: 75 })).json.error).toBe("invalid");
+  const filed = await call(dresser, "PATCH", `/api/v1/products/${jacketID}`, { category: 716 });
+  expect(filed.json.fields).toEqual(["category"]);
+  expect(filed.json.product.categories).toEqual(coat.category_path);
+  expect(filed.json.product.category).toEqual(coat.category_path);
+  expect(await names("&category=716")).toEqual(["Dresser Coat", "Dresser Jacket"]);
+  // Back to its parent's: the history keeps paths, and undoing puts the chosen one back.
+  expect((await call(dresser, "PATCH", `/api/v1/products/${jacketID}`, { category: null })).json.product.categories).toEqual(parent);
+  expect(await names("&category=716")).toEqual(["Dresser Coat"]);
+  const [cleared] = (await call(dresser, "GET", `/api/v1/products/${jacketID}/history`)).json.entries;
+  expect(cleared.changes.category).toEqual({ from: coat.category_path, to: null });
+  expect((await call(dresser, "POST", `/api/v1/products/${jacketID}/history/${cleared.id}/revert`, {})).json.product.categories).toEqual(coat.category_path);
+
   // The library shows them too.
   expect((await call(dresser, "PUT", `/api/v1/library/${coatID}`)).status).toBe(200);
   expect((await call(dresser, "GET", "/api/v1/library")).json.library[0].product).toMatchObject({ image: coat.product_image });